Math / Algebra

QuestionSolve for $n$ 1) $8 \times n=280$ 2) $\underline{n \times 9}=20.7$ 3) $13 \times n=156$ 4) $\frac{3}{8} \times n=15$
Find the value of $n$ . Check your answer. 5) $12 \frac{3}{5} \underline{n}=$ $\overline{15} 5$ 13) $100=\frac{n}{5}$ 9) $\frac{14}{56}=\frac{n}{12}$ Text Predictions: On Th Accessibility: Unavailable Focus

Studdy Solution

STEP 1

1. Each equation is independent and requires solving for $n$ .
2. The operations involved are basic algebraic operations, including multiplication, division, and fractions.
3. Each solution should be verified by substituting back into the original equation.

STEP 2

1. Solve each equation for $n$ .
2. Check each solution by substituting back into the original equation.

STEP 3

For equation 1) $8 \times n = 280$ :
Divide both sides by 8 to isolate $n$ :
$n = \frac{280}{8}$

STEP 4

Calculate the division:
$n = 35$

STEP 5

Check the solution for equation 1 by substituting $n = 35$ back into the original equation:
$8 \times 35 = 280$
The left-hand side equals the right-hand side, so the solution is correct.

STEP 6

For equation 2) $n \times 9 = 20.7$ :
Divide both sides by 9 to isolate $n$ :
$n = \frac{20.7}{9}$

STEP 7

Calculate the division:
$n = 2.3$

STEP 8

Check the solution for equation 2 by substituting $n = 2.3$ back into the original equation:
$2.3 \times 9 = 20.7$
The left-hand side equals the right-hand side, so the solution is correct.

STEP 9

For equation 3) $13 \times n = 156$ :
Divide both sides by 13 to isolate $n$ :
$n = \frac{156}{13}$

STEP 10

Calculate the division:
$n = 12$

STEP 11

Check the solution for equation 3 by substituting $n = 12$ back into the original equation:
$13 \times 12 = 156$
The left-hand side equals the right-hand side, so the solution is correct.

STEP 12

For equation 4) $\frac{3}{8} \times n = 15$ :
Multiply both sides by the reciprocal of $\frac{3}{8}$ to isolate $n$ :
$n = 15 \times \frac{8}{3}$

STEP 13

Calculate the multiplication:
$n = 40$

STEP 14

Check the solution for equation 4 by substituting $n = 40$ back into the original equation:
$\frac{3}{8} \times 40 = 15$
The left-hand side equals the right-hand side, so the solution is correct.

STEP 15

For equation 5) $12 \frac{3}{5} \times n = 155$ :
Convert the mixed number to an improper fraction: $\frac{63}{5}$ .
Multiply both sides by the reciprocal of $\frac{63}{5}$ to isolate $n$ :
$n = 155 \times \frac{5}{63}$

STEP 16

Calculate the multiplication:
$n = \frac{775}{63} \approx 12.3016$

STEP 17

Check the solution for equation 5 by substituting $n \approx 12.3016$ back into the original equation:
$12 \frac{3}{5} \times 12.3016 \approx 155$
The left-hand side approximately equals the right-hand side, so the solution is correct.

STEP 18

For equation 13) $100 = \frac{n}{5}$ :
Multiply both sides by 5 to isolate $n$ :
$n = 100 \times 5$

STEP 19

Calculate the multiplication:
$n = 500$

STEP 20

Check the solution for equation 13 by substituting $n = 500$ back into the original equation:
$\frac{500}{5} = 100$
The left-hand side equals the right-hand side, so the solution is correct.

STEP 21

For equation 9) $\frac{14}{56} = \frac{n}{12}$ :
Cross-multiply to solve for $n$ :
$14 \times 12 = 56 \times n$

STEP 22

Simplify and solve for $n$ :
$168 = 56n$
Divide both sides by 56:
$n = \frac{168}{56}$

STEP 23

Calculate the division:
$n = 3$

STEP 24

Check the solution for equation 9 by substituting $n = 3$ back into the original equation:
$\frac{14}{56} = \frac{3}{12}$
Both fractions are equivalent, so the solution is correct.

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Studdy Solution

STEP 1

1. Each equation is independent and requires solving for n n n.2. The operations involved are basic algebraic operations, including multiplication, division, and fractions.3. Each solution should be verified by substituting back into the original equation.

STEP 2

1. Solve each equation for n n n.2. Check each solution by substituting back into the original equation.

STEP 3

For equation 1) 8×n=280 8 \times n = 280 8×n=280:Divide both sides by 8 to isolate n n n:n=2808 n = \frac{280}{8} n=8280​

STEP 4

Calculate the division:n=35 n = 35 n=35

STEP 5

Check the solution for equation 1 by substituting n=35 n = 35 n=35 back into the original equation:8×35=280 8 \times 35 = 280 8×35=280The left-hand side equals the right-hand side, so the solution is correct.

STEP 6

For equation 2) n×9=20.7 n \times 9 = 20.7 n×9=20.7:Divide both sides by 9 to isolate n n n:n=20.79 n = \frac{20.7}{9} n=920.7​

STEP 7

Calculate the division:n=2.3 n = 2.3 n=2.3

STEP 8

Check the solution for equation 2 by substituting n=2.3 n = 2.3 n=2.3 back into the original equation:2.3×9=20.7 2.3 \times 9 = 20.7 2.3×9=20.7The left-hand side equals the right-hand side, so the solution is correct.

STEP 9

For equation 3) 13×n=156 13 \times n = 156 13×n=156:Divide both sides by 13 to isolate n n n:n=15613 n = \frac{156}{13} n=13156​

STEP 10

Calculate the division:n=12 n = 12 n=12

STEP 11

Check the solution for equation 3 by substituting n=12 n = 12 n=12 back into the original equation:13×12=156 13 \times 12 = 156 13×12=156The left-hand side equals the right-hand side, so the solution is correct.

STEP 12

For equation 4) 38×n=15 \frac{3}{8} \times n = 15 83​×n=15:Multiply both sides by the reciprocal of 38\frac{3}{8}83​ to isolate n n n:n=15×83 n = 15 \times \frac{8}{3} n=15×38​

STEP 13

Calculate the multiplication:n=40 n = 40 n=40

STEP 14

Check the solution for equation 4 by substituting n=40 n = 40 n=40 back into the original equation:38×40=15 \frac{3}{8} \times 40 = 15 83​×40=15The left-hand side equals the right-hand side, so the solution is correct.

STEP 15

For equation 5) 1235×n=155 12 \frac{3}{5} \times n = 155 1253​×n=155:Convert the mixed number to an improper fraction: 635 \frac{63}{5} 563​.Multiply both sides by the reciprocal of 635\frac{63}{5}563​ to isolate n n n:n=155×563 n = 155 \times \frac{5}{63} n=155×635​

STEP 16

Calculate the multiplication:n=77563≈12.3016 n = \frac{775}{63} \approx 12.3016 n=63775​≈12.3016

STEP 17

Check the solution for equation 5 by substituting n≈12.3016 n \approx 12.3016 n≈12.3016 back into the original equation:1235×12.3016≈155 12 \frac{3}{5} \times 12.3016 \approx 155 1253​×12.3016≈155The left-hand side approximately equals the right-hand side, so the solution is correct.

STEP 18

For equation 13) 100=n5 100 = \frac{n}{5} 100=5n​:Multiply both sides by 5 to isolate n n n:n=100×5 n = 100 \times 5 n=100×5

STEP 19

Calculate the multiplication:n=500 n = 500 n=500

STEP 20

Check the solution for equation 13 by substituting n=500 n = 500 n=500 back into the original equation:5005=100 \frac{500}{5} = 100 5500​=100The left-hand side equals the right-hand side, so the solution is correct.

STEP 21

For equation 9) 1456=n12 \frac{14}{56} = \frac{n}{12} 5614​=12n​:Cross-multiply to solve for n n n:14×12=56×n 14 \times 12 = 56 \times n 14×12=56×n

STEP 22

Simplify and solve for n n n:168=56n 168 = 56n 168=56nDivide both sides by 56:n=16856 n = \frac{168}{56} n=56168​

STEP 23

Calculate the division:n=3 n = 3 n=3

STEP 24

Check the solution for equation 9 by substituting n=3 n = 3 n=3 back into the original equation:1456=312 \frac{14}{56} = \frac{3}{12} 5614​=123​Both fractions are equivalent, so the solution is correct.

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1. Each equation is independent and requires solving for $n$ .
2. The operations involved are basic algebraic operations, including multiplication, division, and fractions.
3. Each solution should be verified by substituting back into the original equation.

1. Solve each equation for $n$ .
2. Check each solution by substituting back into the original equation.

For equation 1) $8 \times n = 280$ :
Divide both sides by 8 to isolate $n$ :
$n = \frac{280}{8}$

Calculate the division:
$n = 35$

Check the solution for equation 1 by substituting $n = 35$ back into the original equation:
$8 \times 35 = 280$
The left-hand side equals the right-hand side, so the solution is correct.

For equation 2) $n \times 9 = 20.7$ :
Divide both sides by 9 to isolate $n$ :
$n = \frac{20.7}{9}$

Calculate the division:
$n = 2.3$

Check the solution for equation 2 by substituting $n = 2.3$ back into the original equation:
$2.3 \times 9 = 20.7$
The left-hand side equals the right-hand side, so the solution is correct.

For equation 3) $13 \times n = 156$ :
Divide both sides by 13 to isolate $n$ :
$n = \frac{156}{13}$

Calculate the division:
$n = 12$

Check the solution for equation 3 by substituting $n = 12$ back into the original equation:
$13 \times 12 = 156$
The left-hand side equals the right-hand side, so the solution is correct.

For equation 4) $\frac{3}{8} \times n = 15$ :
Multiply both sides by the reciprocal of $\frac{3}{8}$ to isolate $n$ :
$n = 15 \times \frac{8}{3}$

Calculate the multiplication:
$n = 40$

Check the solution for equation 4 by substituting $n = 40$ back into the original equation:
$\frac{3}{8} \times 40 = 15$
The left-hand side equals the right-hand side, so the solution is correct.

For equation 5) $12 \frac{3}{5} \times n = 155$ :
Convert the mixed number to an improper fraction: $\frac{63}{5}$ .
Multiply both sides by the reciprocal of $\frac{63}{5}$ to isolate $n$ :
$n = 155 \times \frac{5}{63}$

Calculate the multiplication:
$n = \frac{775}{63} \approx 12.3016$

Check the solution for equation 5 by substituting $n \approx 12.3016$ back into the original equation:
$12 \frac{3}{5} \times 12.3016 \approx 155$
The left-hand side approximately equals the right-hand side, so the solution is correct.

For equation 13) $100 = \frac{n}{5}$ :
Multiply both sides by 5 to isolate $n$ :
$n = 100 \times 5$

Calculate the multiplication:
$n = 500$

Check the solution for equation 13 by substituting $n = 500$ back into the original equation:
$\frac{500}{5} = 100$
The left-hand side equals the right-hand side, so the solution is correct.

For equation 9) $\frac{14}{56} = \frac{n}{12}$ :
Cross-multiply to solve for $n$ :
$14 \times 12 = 56 \times n$

Simplify and solve for $n$ :
$168 = 56n$
Divide both sides by 56:
$n = \frac{168}{56}$

Calculate the division:
$n = 3$

Check the solution for equation 9 by substituting $n = 3$ back into the original equation:
$\frac{14}{56} = \frac{3}{12}$
Both fractions are equivalent, so the solution is correct.